Graphical rendering is the computer implemented process of generating images from simulated models in a scene, and is typically performed by software executed by one or more processors in a computing system. Of paramount importance in proper graphical rendering is effectively representing the behavior of light in the generated images. As such, various techniques have been developed to accurately and efficiently simulate the transport of light within the field of computer graphics rendering. Conventionally, the transportation of light may be simulated by light transport simulation engines, consisting of software and/or hardware that may employ one or more modeling techniques to model the behavior of light particles in an image.
One such modeling technique is known as ray tracing, which aims to simulate the natural flow of light, interpreted as particles, by tracing rays in light transport paths. Often, ray tracing methods involve using a class of numerical algorithms known as Monte Carlo methods that rely on repeated random sampling to compute their results. Even more recently, sampling techniques using low discrepancy sequences have been developed which are often preferred over random sampling, as they ensure a more uniform coverage and normally have a faster order of convergence than simulations using random or pseudorandom sequences (such as simulations generated using Monte Carlo methods). Methods based on low discrepancy sequences are known as quasi-Monte Carlo methods, and applications involving such methods are known as quasi-Monte Carlo applications.
A particular application of ray tracing is known as path tracing, which attempts to simulate the physical behavior of light as accurately as possible. One such path tracing technique utilizes “Sobol' sequences” (also called (t, s)-sequences in base 2), a widely used low discrepancy sequence in quasi-Monte Carlo applications. These sequences use a base of two to form successively finer uniform partitions of the unit interval, and then reorder the coordinates in each dimension.
According to a popular technique of path tracing, sampled points are created by exploiting the stratification properties of the Sobol' sequence and transforming the points accordingly. While its construction is very efficient, it is known that low-dimensional projections of the Sobol' points can reveal correlation patterns, especially for rather small subsets of the sequence. Applied to problems with low-dimensional structure, such as light transport simulation, these correlation patterns can unfortunately become visible as transitionary but distracting artifacts, particularly during progressive simulation. While it is guaranteed that the artifacts vanish, they do so slowly. These problems are due to correlations in low-dimensional projections of the Sobol' sequence. Although considerable research and effort has been dedicated to improving the Sobol' sequence, issues in light transport simulation remain.